Matching the bisection bound for routing and sorting on the mesh
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Optimal sorting on mesh-connected processor arrays
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Improved bounds for routing and sorting on multi-dimensional meshes
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Many-to-one packet routing on grids
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing and Sorting
IEEE Transactions on Computers
Improved bounds for all optical routing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Derandomizing algorithms for routing and sorting on meshes
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Algorithms and Average Time Bounds of Sorting on a Mesh-Connected Computer
IEEE Transactions on Parallel and Distributed Systems
Optimal Sorting Algorithms on Incomplete Meshes with Arbitrary Fault Patterns
ICPP '97 Proceedings of the international Conference on Parallel Processing
Fault tolerant routing in toroidal networks
PAS '95 Proceedings of the First Aizu International Symposium on Parallel Algorithms/Architecture Synthesis
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Sorting and routing on r-dimensional n*. . .*n grids of processors is studied. Deterministic algorithms are presented for h-h problems, hor=1, where each processor initially and finally contains h elements. It is shown that the classical 1-1 sorting can be solved with (2r-1.5)n+o(n) transport steps, i.e. in about 2.5n steps for r=2. The general h-h sorting problem, hor=4r-4 can be solved within a number of transport steps that asymptotically differs by a factor of at most 3 from the trivial bisection bound. Furthermore, the bisection bound is asymptotically tight for sequences of h permutation routing problems, h=4cr, cor=1, and for so-called offline routing.